& Magnus, J.R. (1999). The sensitivity of OLS when the variance matrix is (partially) unknown. Journal of Econometrics 92
Author(s) from Durham
We consider the standard linear regression model y=Xβ+u with all standard assumptions, except that the variance matrix is assumed to be σ2Ω(θ), where Ω depends on m unknown parameters Full-size image (<1 K). Our interest lies exclusively in the mean parameters β or Xβ. We introduce a new sensitivity statistic (B1) which is designed to decide whether ŷ (or Full-size image (<1 K)) is sensitive to covariance misspecification. We show that the Durbin–Watson test is inappropriate in this context, because it measures the sensitivity of Full-size image (<1 K) to covariance misspecification. Our results demonstrate that the estimator Full-size image (<1 K) and the predictor ŷ are not very sensitive to covariance misspecification. The statistic is easy to use and performs well even in cases where it is not strictly applicable.